Graduate Management Admission Test (GMAT) Practice Test

When encountering √x in the denominator, what should you do?

1. Leave it as is

2. Multiply by 1

3. Multiply by √x / √x

4. Divide by √x

The correct answer is: Multiply by √x / √x

When √x appears in the denominator of a fraction, the common practice in mathematics is to rationalize the denominator. This means transforming the fraction so that the denominator no longer contains any radical expressions. The method of multiplying by √x / √x serves this purpose effectively. By doing so, you are essentially multiplying the numerator and the denominator by the same quantity, which is effectively equal to 1. This operation will allow you to eliminate the square root from the denominator. For example, if you have a fraction like \( \frac{a}{\sqrt{x}} \) and you multiply both the numerator and the denominator by √x, the expression becomes \( \frac{a \cdot \sqrt{x}}{\sqrt{x} \cdot \sqrt{x}} = \frac{a\sqrt{x}}{x} \). This transformation results in a cleaner and more manageable expression without a radical in the denominator, which is typically preferred in mathematical conventions. Thus, the recommended action of multiplying by √x / √x successfully rationalizes the denominator, making it the correct approach when dealing with √x in that position.